Finally, I am getting closer to staining and painting the walls.(had to take brake from this crazy project) When my place went through the condo conversion new drywall was overlaid over the old plaster which made the window frames look almost embedded into the wall. I decided to add extra wood so at least the spacing looks good. Attached are the photos how it looks now.
I have a question about using the joint compound to fix the holes.
What joint compound would you recommend?
On the right side of the window I was planing to just use the standard multipurpose joint compound. I though about caulk, but I think due to the fact that the walls are uneven I thought that joint compound would just work fine. On the left side of the frame where i have the wall I have bigger holes, and i wonder what to use to fill those? Should i just stick some paper inside and go over with the compound or use some kind of spray foam?

If you have the wood prepped to where you want it now, or close, I would think about going ahead and finishing it before you try to seam the dry wall to it. Or at least get it to the point right before the final coat of finish clear.
Having sealed wood to work to, rather than raw/cleaned wood is easier to me. You don't have to worry about the wood absorbing traces of Sheetrock or caulk if its sealed.

Multipurpose mud would probably be fine for the big crack on the left. I've seen that done in several houses. With that thick/wide of an application, it can crack easily, but there's not usually a lot if movement on interior trim. I have put a thin layer or caulk over wider muddled cracks like that to provide some flexibility.

Filling it completely with an elastomeric caulk, is maybe more stable overall, but its harder to get it looking smooth, hard to sand caulk.

Either way, the spray foam, even the non expanding kind, is difficult to use for an application like yours without making a mess.
Foam filler rope will give you a solid, and even, foam backing for your mud/caulk. It comes in different diameters, you want it a little bigger than the crack so it fits snugly.... Or just stuff some paper towels in it.

This is a piece of the 3/4 (I think), it comes in small rolls. I carry it because its handy and gives you a uniform backing if you get it in right.

More people and contractors burn down old buildings using heat guns and torches than probably anything else, not only is the fire risk great, but you are essentially burning lead paint and the fumes will be toxic.

Liquid stripper is what to use, or replace the flat boards if that's all they are.
Sometimes it's just easier and quicker to replace centain boards than trying to strip 30 layers of lead paint off a board that was nothing but a low priced trashy paint grade pine or spruce to begin with that was meant to be painted.

A co-worker tried to give me a pickuptruck full of old salvaged boards from a hotel's interior door openigns and windows, they were flat but fluted, 5" x about 7' long, but just cheap softwood under layers of old paint.
As a test I tried stripping the paint off one, it took a quart of stripper to get it clean! for what the stripper cost to strip each board I could buy new OAK boards and run a router on them, and that's what I did.

Joe is right, you are pushing chain. There are labors of love and there are forlorn hopes, you have the latter. You cam Mimic what you have with a router and a nice small router table with round over bits and a couple others. The clear pine you will need will probaby cost less than all the stripper you will need. Some things simply are not worth it.

Exactly, this looks like just the cheapest paint grade softwood they used because they were going to paint it, for what the cost of stripper is, you can replace with much better hardwood like oak.
I can get real nice white oak for about $2.90 a bd foot, I can also get walnut, cherry, poplar.

More people and contractors burn down old buildings using heat guns and torches than probably anything else, not only is the fire risk great, but you are essentially burning lead paint and the fumes will be toxic.

Liquid stripper is what to use, or replace the flat boards if that's all they are.
Sometimes it's just easier and quicker to replace centain boards than trying to strip 30 layers of lead paint off a board that was nothing but a low priced trashy paint grade pine or spruce to begin with that was meant to be painted.

I am a contractor and have never burned down a building with a heat gun yet. Not saying this should encourage you to go out and get one thinking you could not start a fire.

Lead fumes are no more toxic than most of the other stuff you would vaporize. Lead is a heavy metal. It will be not be in the vapors but what you scrape off.

Your goal in stripping paint or other finish should always be to use the method that creates the least amount of heat---from either chemical or physical abrasion (sandpaper spinning at high speed).

1. You would be really surprised what you can sometimes get off with a SHARP drag type scraper. Or a contour shaped scraper set. Then sandpaper.

2. Try a modern, safe, chemical gel stripper.

3. Some of the old ones that worked fast and quick had vapors that were explosive.

4. Buy or rent an infrared stripper. They will melt layers of paint without hurthing the substrate material.

If you have the wood prepped to where you want it now, or close, I would think about going ahead and finishing it before you try to seam the dry wall to it. Or at least get it to the point right before the final coat of finish clear.
Having sealed wood to work to, rather than raw/cleaned wood is easier to me. You don't have to worry about the wood absorbing traces of Sheetrock or caulk if its sealed.

Multipurpose mud would probably be fine for the big crack on the left. I've seen that done in several houses. With that thick/wide of an application, it can crack easily, but there's not usually a lot if movement on interior trim. I have put a thin layer or caulk over wider muddled cracks like that to provide some flexibility.

Filling it completely with an elastomeric caulk, is maybe more stable overall, but its harder to get it looking smooth, hard to sand caulk.

Either way, the spray foam, even the non expanding kind, is difficult to use for an application like yours without making a mess.
Foam filler rope will give you a solid, and even, foam backing for your mud/caulk. It comes in different diameters, you want it a little bigger than the crack so it fits snugly.... Or just stuff some paper towels in it.

This is a piece of the 3/4 (I think), it comes in small rolls. I carry it because its handy and gives you a uniform backing if you get it in right.

I am a contractor and have never burned down a building with a heat gun yet.

Good, but these folks DID, and others are sure to in the future:

On November 20, 2001, contractors using open flame torches and heat guns on the cupola supporting the building's gold dome accidentally set the cupola on fire. Golden smoke rose from the Old Capitol Building as the dome burned.
The bell at the top of the Old Capitol was irreparably damaged, the dome was destroyed, and the tens of thousands of gallons of water used to douse the blaze caused major damage. The University of Iowa later settled a lawsuit with the contractors for $1.9 million

Mar 30, 2012 – Division chief Lyle Schwartz said the fire was caused by the occupant after he was stripping paint on the exterior wall with a heat gun.

A heat gun being used by a contractor to dry plaster a wall in a Scarsdale home overheated, causing wallpaper or a drop cloth to catch fire, said Scarsdale Fire...

Heat gun causes fire A house at 1408 E. Maine was damaged by fire about 12:39 p.m. Sunday.
Fire Capt. Mike Sears said the occupant was scraping paint with a heat gun and it got too hot. The fire started in the attic over the front room.
Firefighters had to remove some siding and the living room sustained damage. There were no injuries.

Feb 1, 2013 – METHUEN — A heat gun being used to defrost a freezer caused a fire that destroyed a one-car, detached garage at 19 Lexington Ave. around

Aug 29, 2011 – SWANTON — An accidental fire that destroyed a Swanton Hill Road residence Sunday was caused by a heat gun that ignited combustibles, ...Mar 5, 2013 – The Town of Beloit Fire Department battled a blaze Monday morning after someone tried to warm up his frozen water pipes at his mobile home ...

Oct 25, 2009 – Authorities say a heat gun used to remove paint from a South Bend home was the cause of a minor fire early Sunday. Fire crews were sent to ...
Sep 15, 2010 – After last year's fire that I started while heat gunning the exterior of our 1888 Victorian, I started researching alternative methods of paint removal...

The Dangers Associated with Torches, Heat Guns, and other Thermal Devices for Paint Removal. Updated July ... Buildings catch fire because of these practices. Irreplaceable ... ignited and a fire started in the room adjacent to the Oval Officewww.dhr.virginia.gov/pdf_files/BurningPaint1.PDF‎

www.odt.co.nz
Mar 22, 2013 – ... after his paint-stripping heat gun set his bathroom on fire yesterday ... It appeared the fire was started in the bathroom's window-sill

Jul 11, 2011 – CLINTON — A house fire at 70 Center St. which caused extensive damage ... revealed that somebody was using a heat gun to remove old paint.

Exposure to lead-paint dust or chips can cause serious health problems. ....Heat guns pose a fire hazard, and make lead dust and vapors, so they should be ...www.health.ny.gov › Lead‎

May 26, 2013 – Investigators determined that a heat gun caused a Sunday fire that damaged a Hill Avenue home, according to a news release from Police Sgt.

The danger is greater on old buildings. Flammable debris, including animal nests, sawdust, lint, and cobwebs, accumulates in joist pockets, attics, and other recesses. This debris can be easily ignited by blowtorches, and it can also be ignited by the lower temperatures created by heat plates or heat guns. Fires started in such recesses can smolder for hours before flames break through to the surface.Even if the surface to be stripped of paint is a non flammable material, such as metal or masonry, torches or heat guns can ignite nearby flammable materials. The fire at the Stonewall Jackson School was caused when torches ignited the wood backing behind the metal cornice.If paint removal is indicated, property owners should specify safer measures for removing paint. The Department of the Interior's Preservation Brief no. 10, "Exterior Paint Problems on Historic Woodwork," is available without charge from the Department of Historic Resources. This publication describes the adv antages and disadvantages of a wide range of paint removal techniques.

So i am close to staining, but before i do it i want to make sure i don't screw anything and I don't paint with wrong color. It took me too long to get to this point.
The stain that was used in that room was done by previous owner, and i am trying to replicate the color. All other rooms were done by me, but i had a can of stain that had no label. It just worked for the job.

Attached show old color. When I sand it a little at the point where i want to blend it with new stain I see there is some white color that looks like paint and then bare wood.

What color of the stain it might be? And what type?

My plan is to go with red mahogany, but i am not sure if this is the same? I am curious what is that white stuff? Might it be all in one stain and poly?

I also found some old can with RED OAK color?
Could this color be a red oak?

The test piece of wood i stained seems to look similar but little darker and it does not have any poly yet. For the test i used red mahogany.
I tested on pine and probably my wood is maple?

Attached show old color. When I sand it a little at the point where i want to blend it with new stain I see there is some white color that looks like paint and then bare wood.

What color of the stain it might be? And what type?

My plan is to go with red mahogany, but i am not sure if this is the same? I am curious what is that white stuff? Might it be all in one stain and poly?

I also found some old can with RED OAK color?
Could this color be a red oak?

The test piece of wood i stained seems to look similar but little darker and it does not have any poly yet. For the test i used red mahogany.
I tested on pine and probably my wood is maple?

I mainly prefer Minwax oil stains, and have used both Red oak and Red mohogany, I found them so close to one another in end results they may as well be the same stain, the difference is so slight .

What species of wood you test stain will have a huge difference in the end color, you simply won't get the same color or coverage with maple as red oak, or oak v/s pine.
It's awfull hard to tell what wood this is from pictures like these, I suspect it's likely a softwood and if so then staining softwood is another whole issue due to getting blotchyness. I've used a stain controller on poplar, it helps even things out.

Here's Minwax red mohogany oil stain on white oak, I wouldn't hold the color to perfection since it's a bit redder than this in person.
Your trim also likely has varnish on it which has turned color a bit too, but this looks close:

I mainly prefer Minwax oil stains, and have used both Red oak and Red mohogany, I found them so close to one another in end results they may as well be the same stain, the difference is so slight .

What species of wood you test stain will have a huge difference in the end color, you simply won't get the same color or coverage with maple as red oak, or oak v/s pine.
It's awfull hard to tell what wood this is from pictures like these, I suspect it's likely a softwood and if so then staining softwood is another whole issue due to getting blotchyness. I've used a stain controller on poplar, it helps even things out.

Here's Minwax red mohogany oil stain on white oak, I wouldn't hold the color to perfection since it's a bit redder than this in person.
Your trim also likely has varnish on it which has turned color a bit too, but this looks close:

Yes, I also want to stick to MinWax as it is known brand and will never disappear so i can buy same color at later time.
The wood on left is a piece of pine bought at home depot.
The original wood is probably maple? (I am not an expert so no idea)

So what is that white stuff?
Is it just the varnish?

Would the wood look reddish with the varnish?
And with every layer it gets more colorful?
The stain i have is like 7 years old, but the box looks like new and was full, so I wonder if i should get a new one?
I plan to use clear semi gloss varnish on it.

i did more experimentation and turns out that there was lots of color at the bottom of the can that did not mix through shaking. I mixed it by hand and now i can get lighter reddish color. The 1st and 2nd (counting from left) is actually same color as 5th. (red Mahogany minwax) The 3rd and 4th is old stain i found called Rich Mahogany by old master. I will go with 5th and semi gloss Polyurethane.

I asked question about white stuff on wood forums and i was told:
"
The white looks like the base color for wood graining to me. It's essentially paint made to look like wood done with a glaze that someone paints the grain on. If that is what it is the wood is first painted white to cover the natural wood then the lighter color of the woodgrain is painted on and then the dark part of the grain is painted on to simulate real wood grain. If you are going back with a oil stain then it's important to get all of the paint off.
"

I removed all of it where i want to stain to draw a line between old and new stain so some day at later time i will redo the other part of the door frame, but for now i want to finish this little room as doing stuff after hours takes forever.

Yes, I also want to stick to MinWax as it is known brand and will never disappear so i can buy same color at later time.
The wood on left is a piece of pine bought at home depot.
The original wood is probably maple? (I am not an expert so no idea)

So what is that white stuff?
Is it just the varnish?

Would the wood look reddish with the varnish?
And with every layer it gets more colorful?
The stain i have is like 7 years old, but the box looks like new and was full, so I wonder if i should get a new one?
I plan to use clear semi gloss varnish on it.

The white stuff? you mean sapwood? boards will have sapwood on them and it doesn't take the stain the same as the rest. Or it could be as someone else said, some kind of woodgraining base color, if you can scrape or sand it off that's what it is, if it goes into the wood itself it's sapwood or discoloration in the board itself.
Still hard to tell on the wood species, easier to tell by how heavy the actual board is, but then youn you need to be familiar with the different woods to use that method.
How the board is cut- qtr sawn, flat, rift can also confuse the eye.
If you can't hammer a nail into that board without bending it, it's hardwood, so if you see any common nails sticking out like some use to hang coats on etc, it's probably softwood because trying to get a nail into maple or oak with a hammer is like trying to nail a board to a concrete wall.

I would not use varnish, it takes forever and a day to dry and stays sticky till it does, I prefer the water based polyurethane and it has excellent reviews. You can put a coat on and it's dry in an hour or less, no fumes.
Varnish tends to make wood look amber not reddish, you might be thinking of orange shellac which tends to give a color between amber and a slight reddish orange.
Let the STAIN do the coloring, the clear coat do the protecting.

The white stuff? you mean sapwood? boards will have sapwood on them and it doesn't take the stain the same as the rest. Or it could be as someone else said, some kind of woodgraining base color, if you can scrape or sand it off that's what it is, if it goes into the wood itself it's sapwood or discoloration in the board itself.
Still hard to tell on the wood species, easier to tell by how heavy the actual board is, but then youn you need to be familiar with the different woods to use that method.
How the board is cut- qtr sawn, flat, rift can also confuse the eye.
If you can't hammer a nail into that board without bending it, it's hardwood, so if you see any common nails sticking out like some use to hang coats on etc, it's probably softwood because trying to get a nail into maple or oak with a hammer is like trying to nail a board to a concrete wall.

I would not use varnish, it takes forever and a day to dry and stays sticky till it does, I prefer the water based polyurethane and it has excellent reviews. You can put a coat on and it's dry in an hour or less, no fumes.
Varnish tends to make wood look amber not reddish, you might be thinking of orange shellac which tends to give a color between amber and a slight reddish orange.
Let the STAIN do the coloring, the clear coat do the protecting.

Never though about using water based varnish. I still have a can of oil based varnish.

But if your doing one side of the casing and trying to blend it in.. Switching to WB now might not be the best idea. Oil and latex both have some effect on the appearance of the stain, but in totally different ways.

Btw, the white stuff has me stumped..?.. Maybe some old sap that had seeped out under the finish and was exposed when you sanded...